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Monday, January 23, 2012

Free Throws and Hand Size: Are Big Hands Detrimental to Shooting?

Introduction

One of the most common discussions on free throws is how bigger hands make it harder to shoot. Shaq has such big hands, people say, that it's impossible for him to be a good free-throw shooter no matter what his form is or how often he practices. Another player, Rondo, has very large hands, especially for point guard, and people excuse his poor shooting from the foul line and his outside jumpers. If this is true, then we should see a lower percentages as a player's hand size increase.

I think one credible explanation is how the ball is held between someone with (relative to the NBA) small hands and someone with large hands. When taking a free throw most people are able to easily grip the ball with both hands: one to provide the power and one for stability. When your dimensions are like Shaq's, it's harder to balance the ball as you release. Try shooting with a tennis ball for an extreme example. You're entirely using one hand to launch it, and it's generally harder to retain precision in the typical basketball shooting motion. (Of course, the tennis ball's smaller size will help you make the shot.) It's a reasonable explanation, and the hand size-shooting myth is prevalent among NBA fans because it feels right. One can't assume this is true, however, without objectively looking into the matter.

Methodology

In order to systematically test the hypothesis that larger hands lower a player's free-throw percentage, you need lots of data. Fortunately, at the pre-draft combine they started collecting hand size from virtually every player. This was only started in 2010, but that still leaves a huge pool of guys to analyze. I could have also included players who have had measurements released to the public by the team or media; you can find plenty of these "facts" online. However, those are self-selected data and I would be compiling them one at a time, which is too slow of a rate for me.

Over the past two years there were 155 players with hand measurements, but only 21 with over 50 free throw attempts in NBA games. The hand sizes ranged from 11.25 inches long to 7.25 among players. Hand width was also measured but not for every player, so I didn't include it in the study. I did, however, use a few other explanatory variables. Since hand size correlates with height and therefore position, those were both used in the data. I also had age as a variable because players typically improve from the line as they get older, although these players are all rookies or sophomores. The height used was the pre-draft's height without shoes because the inflated with shoes number or whatever a team lists has more variation -- some guys gain an inch for their shoes, and some two.

Results

The first results I'll discuss are for players with over 50 attempts and treating each player as a separate datum. Free-throw percentage was the dependent variable, and hand size, height, position, and age were tested as the independent variables in a linear regression. I tried every combination of the independent variables, and in every case hand size statistically insignificant. Even with just one independent variable the p-value for hand length -- it's the probability that hand length has zero effect on FT% -- was only 0.111. For reference, 0.05 is taken as statistically significant, and hand size correlates with position well enough that you'd think there'd be enough of a correlation for a better result. By contrast, using just height, the p-value was 0.016 and the R-squared value 0.27, meaning 27% of the variation in free-throw shooting percentage was explained by height alone.

The table below contains the 21 players with over 50 attempts arranged by hand size. There's a bit of a pattern where most of the best shooters have smaller hands, but it's not perfect. Aminu, in particular, has huge hands but he's shot well from the line. Likewise, Vasquez has tiny hands for an NBA player but he's been terrible. I also want to note that 21 samples are not large enough for a conclusive study, and in couple years there should be enough data. However, there is no overwhelming evidence to support the claim that hand size has a negative effect on free-throw shooting, and I think that's a fascinating preliminary result.

Player

Free-throw %

Hand length (in)

Height w/out shoes

Larry Sanders

57.1

9.75

6' 9.25"

Al Farouq Aminu

79.6

9.5

6' 7.25"

Ekpe Udoh

64.7

9.5

6' 8.75"

DeMarcus Cousins

68.7

9.25

6' 9.5"

Ed Davis

59.0

9.25

6' 9"

Marshon Brooks

77.4

9

6' 4.25"

Trevor Booker

65.3

9

6' 6.25"

Wesley Johnson

68.6

9

6' 6.25"

Derrick Favors

58.6

8.75

6' 8.75"

Evan Turner

50.6

8.75

6' 5.75"

Greg Monroe

66.4

8.75

6' 9.75"

Xavier Henry

63.5

8.75

6' 5.25"

Eric Bledsoe

74.4

8.5

6' 0.25"

Gordon Hayward

71.9

8.5

6' 6.75"

Manny Harris

76.3

8.5

6' 4"

Paul George

77.9

8.5

6' 7.75"

John Wall

76.7

8.25

6' 2.75"

Kyrie Irving

80.0

8.25

6' 1.75"

Jordan Crawford

82.9

8

6' 3"

Kemba Walker

74.5

8

5' 11.5"

Greivis Vasquez

61.5

7.75

6' 4.75"

Perhaps a better method is to pool each free throw attempt into a hand size measurement. That way a rookie who only plays in a blowout will have his ten attempts be used with the rest of the group of players with his hand length. Luckily, hands were measured in discrete units instead of something more exact like 8.425" and there are only nine categories. The linear regression based on one independent variable, hand size, output a p-value of 0.326 and an R-squared of 0.137. Basically, there was no correlation, and the graph below illustrates the point. There isn't any designation of point guard versus centers, but pundits claim someone like Rondo shoots so poorly because of his large hands. One problem, however, with a smaller than ideal data set is that players with high attempts like John Wall skew the results, and that's why you're seeing such different results for each size.

Hand length (in)

Free-throw %

9.75

58.2

9.5

73.6

9.25

65.8

9

71.6

8.75

59.9

8.5

74.3

8.25

75.6

8

81.3

7.75

62.9

Another approach I tried was grouping the results by position and applying linear regression to each position. Unfortunately, there aren't enough players yet with hand measurements to subdivide the data even when lowering the free throw requirement to 20 attempts. The results, however, were so one-sided that I doubt more data would reveal a statistical significance between hand size within positions. Point guards, for example, a group known for their sweet shooting, had a tiny R-squared value of 0.0529 and a p-value for the hand length coefficient of 0.523. R-squared, to reiterate, is saying hand length only explains 5% of the variation in free-throw percentage among point guards, and that's a abhorrent result. There were only 10 point guards to qualify, but the same was true of each position. Again, there was no evidence to conclude that hand size was a significant variable in determining free-throw percentage. To illustrate the lack of association between size and free throws, Iman Shumpert was more of a combo guard so he wasn't included, but he has larger hands than any point, yet he's at 22/24 for the year.

Conclusion

The NBA athletes we see on TV are undeniably talented and earning more money than most of us will ever accrue in our lives. When we see a player making $10 million a year miss a free throw -- a shot even little kids can make -- we're angry and baffled. Surely he's been practicing for years, so why is he shooting 60% for the season? In asking that question some seek answers about how some players aren't able to make them during the flow of the game or that these athletes' hands are too big to accurately shoot. We can find examples like Duncan, who clearly has worked on his shot but often shoots under 70%, to fit our theory and confirm our own perceptions, but there are also counter-examples. Pau Gasol has enormous hands and palms the ball with ease, but he has an accurate jump shot and cleared 80% for the season multiple times. John Stockton is a point guard with large mitts, and he's at 82.6% for his career with a good three-point shot. Michael Jordan, known for using his big hands to dunk with flair, is even better at 83.5%.

The inclusion of hand size measurements for nearly every drafted player recently will lead to a better data set, and at the end of the year I'll redo the regression to see if anything changes. There are a couple other hypotheses that need to be tested. Maybe there's a hand size limit beyond which percentage plunges, but we don't have enough information for that yet. The players in the data are all very young and the results could change once they improve or, even their hand size is so problematic, flatline at a poor number. Within a couple of years we could get a definitive answer as more guys get measured and the ones that already have rack up attempts. However, based on the data right now, there is no evidence to support the hypothesis that hand size negatively affects free-throw percentage.

3 comments:

Pretty interesting and exactly what I was looking for as a Laker fan assessing the Lakers' abysmal FT shooting last game, and dwight howard in particular. Near the end of the year, so I hpe we get the regression redo